Given that the tangent equation at any point (x0, Y0) in the image of function f (x) (x belongs to R) is y-y0 = (x0-2) (x0 ^ 2-1) (x-x0), then the monotonicity of function f (x) is

F '(x) = (X-2) (x ^ 2-1) so the function is monotonically increasing in the interval | 2, positive infinity | u | - 1,1 | and decreasing in the interval (negative infinity, - 1) U (- 1,2)

Matlab solution: let the function f (x) = x + sin2x, x0 = π / 2, require (1) draw the curve of y = f (x) in the interval of x0 ≤ x ≤ x0 + π / 2
(2) Keep x0 fixed and find the quotient difference Q (H) = (f (x0 + H) - f (x0)) / h as a function of H;
(3) Find that h → 0 is the limit of Q (H);
(4) For H = 3, 2 and 1, define the secant y = f (x0) + Q * (x-xo) and draw the secant;
(5) Draw the tangent of the curve at the point x0 = π / 2.

x0=2*pi;
x=x0:0.001:x0+pi/2;
y=x+sin(2*x);
plot(x,y);
grid;

3. Let f (x) be defined on the open interval I, I, and the point (x0, f (x0)) be the inflection point of the curve y = f (x), then there must be () A. on both sides of the point (x0, f (x0)), the curve y = f (x) is concave or convex. B. when x0, the curve y = f (x) is convex (or concave). C.xf (x0). D.xf (x0) and when x > x0, f (x)

Choose B, and the concave and convex ends of inflection point are opposite

The convex interval of the curve f (x) = ln x is: the inflection point of the curve f (x) = x3-x is: the extreme point of the function f (x) = ln (x2 + 1) is:

(1) Firstly, the definition domain of function f (x) = LNX is (0, + ∞);
f’’(x)=-1/x2,
When f '(x) 0, f' (x) > 0, f (x) = ln (x2 + 1) increases monotonically
When x

Solving the problem of oblique triangle
If the lengths of three sides of an obtuse triangle are three continuous natural numbers, then the lengths of the three sides are zero________ .
Please give the important steps of disassembly

Three continuous natural numbers 3.4.5 form a right triangle. So only the continuous natural number less than it can be an obtuse triangle. So the three sides are 2, 3 and 4
therefore
If the lengths of three sides of an obtuse triangle are three continuous natural numbers, then the lengths of the three sides are zero__ 2、3、4_.

What is the volume of a triangle with 10 cm, 8 cm and 6 cm sides?

The figure is two cones with a radius of 6 * 8 / 10 = 4.8 (CM)
Volume: 3.14 * 4.8 * 4.8 * 10 / 3 = 241.152 (cm3)
A: the volume of the figure is 241.152 (cubic centimeter)

As shown in the figure is a right triangle, with ab side as the axis to rotate a circle, the body is a triangle And its volume is Cubic centimeter

With ab as the axis, the volume of the cone is: 13 × 3.14 × 22 × 6 = 13 × 3.14 × 4 × 6 = 25.12 (cubic centimeter); answer: with ab side as the axis, the body is a cone, its volume is 25.12 cubic centimeter. So the answer is: cone, 25.12

What shape of object can be formed by rotating the triangle in the following figure around AB axis? What is its volume in cubic centimeter?
The bottom is 8 cm and the height is 6 cm

It should have a radius of 8
3.14 * 8 * 8 (bottom area) * 6 / 3 = 401.92
A: it can form a cone with a volume of 401.92 cubic centimeters

If the length of the center line of the triangle is known as a, B and C, the length of the triangle can be calculated

Let Tan α = 2, calculate sin α + cos α / sin α - cos α
emergency

It's too simple. It's OK to divide cosa
Sina / cosa = Tana you should know that
And then it's better to put it in
The final result is 3

Given that the tangent equation at any point (x0, Y0) in the image of function f (x) (x belongs to R) is y-y0 = (x0-2) (x0 ^ 2-1) (x-x0), then the monotonicity of function f (x) is